CN109039573B

CN109039573B - CPM signal multi-symbol detection method

Info

Publication number: CN109039573B
Application number: CN201810921321.3A
Authority: CN
Inventors: 周敬权; 郝筱鲲; 王鹏
Original assignee: Chengdu Yeruan Technology Co ltd
Current assignee: Chengdu Yeruan Technology Co ltd
Priority date: 2018-08-14
Filing date: 2018-08-14
Publication date: 2022-03-29
Anticipated expiration: 2038-08-14
Also published as: CN109039573A

Abstract

The invention discloses a CPM signal multi-symbol detection-based method, belonging to the field of continuous phase frequency shift keying signal demodulation; which comprises the following steps of 1: preprocessing a received signal to obtain a baseband complex signal component and generate a local detection sequence; step 2: the baseband complex signal component is sequentially slid according to the packet length N and is subjected to maximum likelihood calculation with a local detection sequence to obtain 2^NMaximum likelihood values and maximum likelihood sequences; and step 3: judging each code element in the maximum likelihood sequence for N times to obtain a primary demodulation signal; and 4, step 4: will 2^NAfter peak detection is carried out on the maximum likelihood values to extract bit synchronization signals, final demodulation signals are output from the preliminary demodulation signals; the invention solves the problems of high calculation complexity and low demodulation performance brought by improving the bit error rate by increasing the matching length in the prior art; the effects of greatly improving the demodulation error rate performance and reducing the complexity of signal demodulation are achieved.

Description

CPM signal multi-symbol detection method

Technical Field

The invention belongs to the field of continuous phase frequency shift keying signal demodulation, and particularly relates to a CPM signal multi-symbol detection method.

Background

The continuous phase modulation CPM has the characteristics of continuous phase, excellent spectrum characteristic and the like; the CPM modulation system is a mode combining channel coding and modulation, and controls the state transition of the next moment by generating a phase state lattice sequence, so that the modulation of information symbols directly has a coding effect, and more redundant symbols are not needed; the CPM modulation system can carry out soft decision on a received signal through Maximum Likelihood Sequence Estimation (MLSE), so that high detection probability under the condition of low signal-to-noise ratio is realized.

For continuous phase modulation CPM, the traditional demodulation method only utilizes information in a single code element, and the demodulation effect is easily limited by a demodulation threshold and interfered by external noise, so that the demodulation performance is reduced under the condition of low signal-to-noise ratio.

With the development of a multi-symbol detection algorithm, the phase memorability characteristics between symbols before and after a CPM signal are combined, and the CPM signal is utilized to carry out multi-symbol detection: when a symbol is received, the judgment is not carried out immediately, and the correlation operation is carried out on the received signal waveform and the locally stored waveform within a plurality of symbol lengths; the demodulation performance of the signal is effectively improved; the traditional multi-symbol detection algorithm is based on the idea of waveform matching, the matching length needs to be increased in order to improve the error rate, but the calculation complexity of the similarity is exponentially increased along with the increase of the length of the matched symbol, so that real-time demodulation cannot be realized under the condition of high symbol rate.

There is therefore a need for a multi-symbol detection method that improves demodulation performance without increasing the matching length.

Disclosure of Invention

The invention aims to: the invention provides a CPM signal multi-symbol detection method, which solves the problems of high computational complexity and low demodulation performance caused by improving the bit error rate by increasing the matching length in the prior art.

The technical scheme adopted by the invention is as follows:

a method for multi-symbol detection based on CPM signal includes the following steps:

step 1: preprocessing a received signal to obtain a baseband complex signal component and generate a local detection sequence;

step 2: the baseband complex signal component is sequentially slid according to the packet length N and is subjected to maximum likelihood calculation with a local detection sequence to obtain 2^NMaximum likelihood values and maximum likelihood sequences;

and step 3: judging each code element in the maximum likelihood sequence for N times to obtain a primary demodulation signal;

and 4, step 4: will 2^NAfter peak detection is performed on the maximum likelihood values to extract the bit synchronization signal, a final demodulation signal is output from the preliminary demodulation signal.

Preferably, the step 1 comprises the steps of:

step 1.1: the received signal is subjected to digital down-conversion to obtain a baseband complex signal component R (t), and the calculation formula is as follows:

R(t)＝cos(θ(t；a′))+jsin(θ(t；a′))

wherein, a 'represents a modulation sequence corresponding to the baseband complex signal component at the time t, and theta (t; a') represents a modulation phase corresponding to the modulation sequence at the time t;

step 1.2: generating local detection sequence 2 based on cordic algorithm^NA local detection signal L_n(t), the calculation formula is as follows:

L_n(t)＝cos(θ(t；a_n))-jsin(θ(t；a_n))

wherein, a_nRepresents L_n(t) the local detection sequence selected, θ (t; a)_n) Indicating the modulation phase corresponding to the local detected sequence at time t.

Preferably, the step 2 comprises the steps of:

step 2.1: generating 2 the baseband complex signal component R (t) according to the packet length N^NA waveform of 2^NEach waveform is respectively equal to 2^NA local detection signal L_n(t) obtaining an instantaneous correlation vector Z by multiplication_nThe calculation formula is as follows:

Z_n(t)＝R(t)·L_n(t)＝cos(θ(t；a′)-θ(t；a_n))+jsin(θ(t；a′)-θ(t；a_n))＝I′_n(t)+jQ′_n(t)

wherein, I'_n(t) represents an instantaneous value of a real part, Q'_n(t) represents instantaneous value of imaginary part;

step 2.2: for instantaneous correlation vector Z_nIntegration is performed to obtain an integral value, and the integral value is subjected to modulo square acquisition 2^NMaximum likelihood values M for the different sequences;

step 2.3: selection 2^NAnd taking the sequence corresponding to the maximum likelihood value in the maximum likelihood values M as the maximum likelihood sequence.

Preferably, the step 3 comprises the steps of:

step 3.1: combining the judgment result of the first bit of each code element in the maximum likelihood sequence with the judgment result of the previous N-1 times, outputting more judged times in 0 and 1, and temporarily storing the result of the next N-1 bits;

step 3.2: and (4) after the step 3.1 is repeated to output the judgment result of each bit of each code element in the maximum likelihood sequence, all the judgment results are taken as preliminary demodulation signals to be output.

Preferably, the step 4 comprises the steps of:

step 4.1: will 2^NCarrying out peak value detection on the maximum likelihood value, and extracting a bit synchronization signal corresponding to the time with the best demodulation performance;

step 4.2: a final demodulation signal is output from the preliminary demodulation signal based on the bit synchronization signal.

Preferably, the peak detection comprises the steps of:

step a: selecting four groups of maximum likelihood values M with the first position of 0 and the first position of 1 for summation to form two groups of related waveforms of 0xx and 1 xx;

step b: recording maximum values or minimum value points generated by two groups of waveforms alternately in the sliding window;

step c: and after the sliding of a plurality of cycles, determining the specific point position of the peak value in a single cycle according to the occurrence time of the extreme value.

In summary, due to the adoption of the technical scheme, the invention has the beneficial effects that:

1. under the condition of not increasing the matching length, the invention slides the input signal and carries out maximum likelihood estimation with the local detection sequence waveform, thereby achieving the purpose of judging each code element for many times, correcting misjudgment caused by noise and avoiding the defect of high calculation complexity caused by increasing the matching length in the prior art; the problems of high calculation complexity and low demodulation performance caused by increasing the matching length to improve the bit error rate in the prior art are solved; the effects of greatly improving the demodulation error rate performance and reducing the complexity of signal demodulation are achieved;

2. the invention corrects the misjudgment code element interfered by noise for a plurality of times of judgment by carrying out sliding correlation on the received waveform; bit synchronization is realized through data temporary storage, and meanwhile, the error rate is reduced;

3. according to the invention, the sampling points in sliding are adjusted according to the actual situation, so that the repeated time consumption can be avoided, and the calculation complexity can be further reduced.

Drawings

In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the embodiments will be briefly described below, it should be understood that the following drawings only illustrate some embodiments of the present invention and therefore should not be considered as limiting the scope, and for those skilled in the art, other related drawings can be obtained according to the drawings without inventive efforts.

FIG. 1 is a block diagram of a multi-symbol detection algorithm of the present invention;

FIG. 2 is a schematic diagram of data sliding according to the present invention;

FIG. 3 is an algorithmic schematic of the sliding input of the present invention;

fig. 4 is a diagram of a maximum likelihood detection reference waveform under the condition of N-3 according to the present invention;

fig. 5 is a graph of likelihood detection characteristics for different signal-to-noise ratios according to the present invention.

Detailed Description

In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the detailed description and specific examples, while indicating the preferred embodiment of the invention, are intended for purposes of illustration only and are not intended to limit the scope of the invention. The components of embodiments of the present invention generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations.

Thus, the following detailed description of the embodiments of the present invention, presented in the figures, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments of the present invention without making any creative effort, shall fall within the protection scope of the present invention.

It is noted that relational terms such as "first" and "second," and the like, may be used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Also, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other identical elements in a process, method, article, or apparatus that comprises the element.

The technical problem is as follows: the problems of high calculation complexity and low demodulation performance caused by increasing the matching length to improve the bit error rate in the prior art are solved.

The technical means is as follows:

The step 1 comprises the following steps:

R(t)＝cos(θ(t；a′))+jsin(θ(t；a′))

L_n(t)＝cos(θ(t；a_n))-jsin(θ(t；a_n))

The step 2 comprises the following steps:

The step 3 comprises the following steps:

The step 4 comprises the following steps:

The peak detection comprises the following steps:

The specific steps of the multi-symbol detection algorithm are as follows:

(1) carrying out digital quadrature down-conversion on a received signal to obtain IQ two-path signal components containing signal phase information, wherein one path is a baseband complex signal component;

(2) generating a local sequence reference waveform according to a binary sequence with a packet length equal to N under the condition of a certain initial phase;

(3) sliding the input baseband complex signal component to generate a plurality of related groups, wherein the length of each group is the number of sampling points of N code elements, and the group number is determined by the sliding distance;

(4) multiplying, summing and modulus-solving a plurality of grouped output signals and a local detection sequence to obtain a group of maximum likelihood values M, and then comparing to determine a maximum likelihood sending sequence;

(5) combining the judgment result of the first bit in the maximum likelihood sending sequence with the judgment result of the previous N-1 times, outputting more judgment times in 0 and 1, and temporarily storing the result of the later N-1 bits;

(6) carrying out peak value detection through the maximum likelihood value to extract a bit synchronization signal, and extracting and outputting a judgment result according to the bit synchronization signal;

the expression of CPM modulation signal is s (t) ═ Acos [2 pi f_ct+θ(t：a_n)+θ₀]，a_nRepresenting a unipolar sequence of outputs, f_cIndicating the carrier frequency used for modulation; the full response carrier phase expression is

Wherein the function q (T-nT) is a time shift and phase increment control factor of the local detection sequence, nT represents the starting time of receiving the nth symbol, and T represents the sampling interval;

after receiving a signal, performing digital down-conversion to obtain a baseband complex signal component r (t), wherein a component of the baseband complex signal component needs to be processed in a real part and an imaginary part in a detection process, and a mathematical expression of the component is r (t) ═ cos (θ (t; a ')) + jsin (θ (t; a')), where a 'represents a modulation sequence corresponding to the baseband complex signal component at time t, and θ (t; a') represents a modulation phase corresponding to the modulation sequence at time t;

if N code elements are detected at a time, the local detection sequence corresponds to 2^NA local detection signal L_n(t) corresponds to 2^NA is_nCorresponding to the phase of the reference signal waveform, its expression is L_n(t)＝cos(θ(t；a_n))-jsin(θ(t；a_n) ); performing CPM modulation by using the expression s (t) e^±jhπt/RThe waveform generation of the local detection sequence needs to set a parameter modulation index h and a code element sampling point number R, the modulation index h is used for determining the frequency corresponding to two code elements of 0 and 1, the sampling point number R is used for determining the continuous point number of each code element in the waveform, the waveform respectively generates a virtual part and a real part by a cordic algorithm and stores the virtual part and the real part, and the imaginary part expression is I_n＝cos(θ(t；a_n) The expression of the real part is Q_n＝sin(θ(t；a_n) ); if N is 3, all possible three bit binary combinations a_nThe total number of the eight types is 000, 001, 010, 011, 100, 101, 110 and 111, all the types a are unified at a time t_nSubstituting into formula L_n(t)＝cos(θ(t；a_n))-jsin(θ)t；a_n) Generate a local sequence reference waveform.

R (t) and L_n(t) performing correlation operation, operating the virtual part and the real part according to complex multiplication, and calculating to obtain an instantaneous correlation vector Z_n：Z_n(t)＝R(t)·L_n(t)＝cos(θ(t；a′)-θ(t；a_n))+jsin(θ(t；a′)-θ(t；a_n))＝I′_n(t)+jQ′_n(t); for instantaneous correlation vector Z_nAnd (4) integrating, and performing modulo square on the integral value to obtain an M value, namely a correlation value between the baseband complex signal and the local reference waveform in the detection sequence length N. When the instantaneous phase of the received signal is the same as or close to the local reference signal phase, i.e., θ (t; a') → θ (t; a:)_n) Of imaginary part Q'_nAlmost zero, leaving only a real part I 'close to 1'_n。

The baseband complex signal component is correlated with the local detection signal to obtain 2^NMaximum likelihood values for different sequences. When theta of the waveform is equal to theta_nWhen Z is_nThe corresponding maximum likelihood value M will be at a maximum, but it will be significantly lower than the maximum likelihood sequence when the waveform phase has a certain deviation.

If the sequence group with the first bit of 0 and the sequence group with the first bit of 1 and the maximum likelihood value are accumulated and output, the maximum likelihood value can gradually reach a peak value in the sliding process, the peak values of the 0 sequence and the 1 sequence can alternately appear, and the alternating rule is consistent with the distribution of the original sequence; the bit synchronization method is that after a plurality of peak value detections, the optimal time for extracting the demodulation result is determined, and the bit synchronization signal is extracted.

If the packet length N is 3, the number R of sample points in a single symbol period is 8, the modulation index h is 0.715, all possible sequence combinations are eight, and each combination generates a 24-point waveform through a sequence generator; eight kinds of reference waveforms are shown in fig. 4, it can be seen that the local 1 and 0 likelihood detection sequences are conjugate to each other, and there are multiple identical waveforms in the imaginary part and the real part, which can avoid the time consumption caused by repetition in a simplified manner.

Will 2^NPeak detection of maximum likelihood valueThe peak detection comprises the following steps:

step a: selecting four groups of maximum likelihood values M with the first position of 0 and the first position of 1 for summation to form two groups of related waveforms of 0xx and 1 xx; step b: recording maximum values or minimum value points generated by two groups of waveforms alternately in the sliding window; step c: and after the sliding of a plurality of cycles, determining the specific point position of the peak value in a single cycle according to the occurrence time of the extreme value. And determining the time with the best demodulation performance by peak detection to extract the bit synchronization signal.

In the process of sliding according to the sampling points, components of 1 and 0 in the sampling points of the sliding window move forwards to be changed alternately, and a signal a' subjected to bit synchronization specifically corresponds to 2^NA is_nOne of the waveforms.

For ease of understanding, the following examples are given: assuming that 01011 exists, each point is sampled eight times, the sequence corresponds to 0000000011111111000000001111111111111111, the sliding window size is 3 symbols and 24 points, and the sliding window takes the following sequence during the sliding process:

000000001111111100000000 (the latter dots also have [1111111111111111])

000000011111111000000001 (front 0 leaving and back entering a 1)

000000111111110000000011

000001111111100000000111

000011111111000000001111

000111111110000000011111

001111111100000000111111

011111111000000001111111

111111110000000011111111

111111100000000111111111

111111000000001111111111

111110000000011111111111

111100000000111111111111

Points behind the sequence enter the window, points ahead leave, alternating 01;

after bit synchronization, these twenty-four points can detect one of the corresponding 000-111:

000000001111111100000000 detect correspondence 010

111111110000000011111111 detect correspondences 101

The likelihood detection of each reference waveform branch can be realized by two complex multipliers or four multipliers, two adders, two accumulators, two squarers and one adder, and the functions of peak counting detection and temporary storage of decision data are added at the tail ends of three parallel branches to complete bit synchronization and reduce the bit error rate.

The decoding performance curves under different signal-to-noise ratios are drawn in fig. 5 by testing according to the above structure, and the signal-to-noise ratio range in the graph is 2dB to-4 dB. According to the demodulation performance of the sliding correlation multi-symbol detection algorithm, the performance is improved by about 1dB (previously, the value is 0.9, and the measured value is 0.99) under a large signal-to-noise ratio compared with the classical multi-symbol detection algorithm, and is improved by about 0.3dB under the condition of a low signal-to-noise ratio compared with the classical multi-symbol detection algorithm.

The technical effects are as follows: under the condition of not increasing the matching length, the invention slides the input signal and carries out maximum likelihood estimation with the local detection sequence waveform, thereby achieving the purpose of judging each code element for many times, correcting misjudgment caused by noise and avoiding the defect of high calculation complexity caused by increasing the matching length in the prior art; the problems of high calculation complexity and low demodulation performance caused by increasing the matching length to improve the bit error rate in the prior art are solved; the effects of greatly improving the demodulation error rate performance and reducing the complexity of signal demodulation are achieved. Intercepting an input waveform, if the input waveform is most relevant to a certain local sequence, if the input waveform is 101, determining that the first bit is 1, and storing the following 01; secondly, intercepting a section of waveform for the second time, wherein the first position is the second position of the previous section, 0 is output when the first position 0 is judged to be matched with the previous judgment, and the subsequent judgment is stored; therefore, one code element is judged for multiple times, and the misjudgment code element interfered by noise is corrected.

The features and properties of the present invention are described in further detail below with reference to examples.

Example 1

In the sliding correlation algorithm, the packet length N is 3, the modulation index h is 0.707, and the number of symbol sampling points R is 6 in the present embodiment, and the specific steps of the CPM signal to perform multi-symbol detection demodulation are as follows:

step 1: local reference waveform mu generated by cordic algorithm according to packet length_n8 groups, each group has 18 points; by defining a rotation mode, setting initial phase angles and vector lengths in parameters, generating two virtual parts and real parts as shown in table 1, and carrying out 12-bit quantization, wherein the two virtual parts and the real parts represent basic waveforms of all possible sequences in a modulation waveform;

TABLE 1

Step 2: the input waveform is down-converted and then time-delayed according to the length of the sliding distance to generate a plurality of waveforms, and the sliding window intercepts the input waveform R according to the relevant length_i(t) length nr;

and step 3: will input signal R_i(t) and local reference waveform L_n(t) performing multi-symbol correlation calculation respectively, wherein 8 calculated correlation values are represented as follows: tau is_i＝[τ_i1，τ_i2，τ_i3，τ_i4，τ_i5，τ_i6，τ_i7，τ_i8](ii) a Any of the correlation values τ_in＝M＝{∑[imag(μ_n)×imag(R_i(t))]+∑[real(μ_n)*real)R_i(t))]}²+{∑[imag(μ_n)×real(R_i(t))]+∑[real(μ_n)*imag(R_i(t))]}²＝I′_n+jQ′_n

And 4, step 4: the maximum likelihood sequence determined after likelihood detection is tau_maxi＝max(τ_i1，τ_i2，τ_i3，τ_i4，τ_i5，τ_i6，τ_i7，τ_i8)；

And 5: the output after three times of temporary storage judgment is tau ═ tau_maxi+τ_maxi+1+τ_maxi+2/3]。

Step 6: adding the likelihood values of the sequence combination with the first bit of 0 and 1 respectively to form two groups of contrast likelihood values tau_1xx＝τ_i1+τ_i2+τ_i3+τ_i4And τ_0xx＝τ_i5+τ_i6+τ_i7+τ_i8Detecting the time of occurrence t of an extreme value of a likelihood value in a sliding window_ext(n) n is the number of detections, and the determination time has the following rule t after a plurality of periodic detections_ext(n+1)＝t_ext(n) + T, T being the symbol sampling interval, it can be determined that the bit synchronization time is T_ext(ii) a And extracting and outputting the judgment result according to the bit synchronization signal to finish multi-symbol detection.

The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents and improvements made within the spirit and principle of the present invention are intended to be included within the scope of the present invention.

Claims

1. A method for multi-symbol detection based on CPM signals, characterized by: the method comprises the following steps:

step 2: the baseband complex signal component sequentially slides according to the packet length N and carries out maximum likelihood calculation with the local detection sequence to obtain 2N maximum likelihood values and maximum likelihood sequences;

and 4, step 4: after peak detection is carried out on the 2N maximum likelihood values to extract bit synchronization signals, final demodulation signals are output from the preliminary demodulation signals;

the step 1 comprises the following steps:

R(t)＝cos(θ(t；a′))+jsin(θ(t；a′))

step 1.2: the cordic algorithm is used to generate local detection sequences, i.e. 2N local detection signals ln (t), and the calculation formula is as follows:

L_n(t)＝cos(θ(t；a_n))-jsin(θ(t；a_n))

wherein, an represents the local detection sequence selected by Ln (t), and theta (t; an) represents the modulation phase corresponding to the local detection sequence at the time t;

the step 2 comprises the following steps:

Zn(t)＝R(t)·Ln(t)＝cos(θ(t；a′)-θ(t；an))+jsin(θ(t；a′)-θ(t；an))＝I′n(t)+jQ′n(t)；

wherein I 'n (t) denotes instantaneous values of the real part, Q' n (t) denotes instantaneous values of the imaginary part;

step 2.3: selection 2^NTaking a sequence corresponding to the maximum likelihood value in the maximum likelihood values M as a maximum likelihood sequence;

the step 3 comprises the following steps:

step 3.2: repeating the step 3.1 to output the judgment result of each bit of each code element in the maximum likelihood sequence, and then outputting all the judgment results as preliminary demodulation signals;

the step 4 comprises the following steps:

step 4.2: outputting a final demodulation signal from the preliminary demodulation signal according to the bit synchronization signal;

the peak detection comprises the following steps:

step c: after sliding in multiple periods, determining specific point positions of peak values in a single period according to the occurrence time of extreme values;

the specific steps of the multi-symbol detection algorithm are as follows:

4) multiplying, summing and modulus-solving a plurality of grouped output signals and a local detection sequence to obtain a group of maximum likelihood values M, and then comparing to determine a maximum likelihood sending sequence;

CPM toneThe expression of the system signal is s (t) ═ Acos [2 pi fct + theta (t: an) + theta 0]An represents the output unipolar sequence, fc represents the carrier frequency employed for modulation; the full response carrier phase expression is

Wherein the function q (T-nT) is a time shift and phase increment control factor of the local detection sequence, nT represents the starting time of receiving the nth symbol, and T represents the sampling interval; after receiving a signal, performing digital down-conversion to obtain a baseband complex signal component r (t), wherein a component of the baseband complex signal component needs to be processed in a real part and an imaginary part in a detection process, and a mathematical expression of the component is r (t) ═ cos (θ (t; a ')) + jsin (θ (t; a')), where a 'represents a modulation sequence corresponding to the baseband complex signal component at time t, and θ (t; a') represents a modulation phase corresponding to the modulation sequence at time t;

if N code elements are detected at a time, the local detection sequence corresponds to 2^NA local detection signal L_n(t) corresponds to 2^NAn corresponds to the phase of the reference signal waveform and is expressed as L_n(t) ═ cos (θ (t; an)) -jsin (θ (t; an)); performing CPM modulation by the expression

The waveform generation of a local detection sequence needs to set a parameter modulation index h and a code element sampling point number R, wherein the modulation index h is used for determining the frequency corresponding to two code elements of 0 and 1, the sampling point number R is used for determining the continuous point number of each code element In the waveform, the waveform respectively generates a virtual part and a real part by a cordic algorithm and stores the virtual part and the real part, and the imaginary part expression is In & cos (theta (t; an)), and the real part expression is Qn & sin (theta (t; an)); if N takes 3, all possible three-bit binary combinations an are eight kinds, namely 000, 001, 010, 011, 100, 101, 110 and 111, with the time t being unified, and each an is substituted into the formula Ln (t) cos (theta (t; an)) -jsin (theta) t; an)) generates a local sequence reference waveform;

performing correlation operation on R (t) and Ln (t), and operating the virtual part and the real part according to complex multiplication to obtain an instantaneous correlation vector Zn: zn (t) ═ r (t) · ln (t) ═ cos (θ (t; a))')-θ(t；an))+jsin(θ(t；a')-θ(t；an))＝I'_n(t)+jQ'_n(t); integrating the instantaneous correlation vector Zn, and performing modulo square on the integral value to obtain an M value which is a correlation value between the baseband complex signal and a local reference waveform in the detection sequence length N; imaginary component Q ' when the instantaneous phase of the received signal is the same as or close to the local reference signal phase, i.e., θ (t; a ') → θ (t; an) '_nAlmost zero, leaving only a real part I 'close to 1'_n；

The baseband complex signal component is correlated with the local detection signal to obtain 2^NMaximum likelihood values for the different sequences; when theta of the waveform is equal to thetan, Z_nThe corresponding maximum likelihood value M will be maximum, but when the waveform phase has a certain deviation, the maximum likelihood value M will be significantly lower than the maximum likelihood sequence;

if the sequence group with the first bit of 0 and the sequence group with the first bit of 1 and the maximum likelihood value are accumulated and output, the maximum likelihood value can gradually reach a peak value in the sliding process, the peak values of the 0 sequence and the 1 sequence can alternately appear, and the alternating rule is consistent with the distribution of the original sequence; the bit synchronization method is that after a plurality of peak value detections, the optimal time for extracting the demodulation result is determined, and a bit synchronization signal is extracted;

will 2^NAnd carrying out peak value detection on the maximum likelihood value, wherein the peak value detection comprises the following steps:

step c: after sliding in multiple periods, the specific point position of the peak value in a single period is determined according to the occurrence time of the extreme value, and the bit synchronization signal is extracted at the time when the demodulation performance is optimal through peak value detection.